Question: Emily is 36 years older than Ishaan. Ten years ago, Emily was 5 times as old as Ishaan. How old is Ishaan now?
Explanation: We can use the given information to write down two equations that describe the ages of Emily and Ishaan. Let Emily's current age be $e$ and Ishaan's current age be $i$ The information in the first sentence can be expressed in the following equation: $e = i + 36$ Ten years ago, Emily was $e - 10$ years old, and Ishaan was $i - 10$ years old. The information in the second sentence can be expressed in the following equation: $e - 10 = 5(i - 10)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$ , it might be easiest to use our first equation for $e$ and substitute it into our second equation. Our first equation is: $e = i + 36$ . Substituting this into our second equation, we get the equation: $(i + 36)$ $-$ $10 = 5(i - 10)$ which combines the information about $i$ from both of our original equations. Simplifying both sides of this equation, we get: $i + 26 = 5 i - 50$ Solving for $i$ , we get: $4 i = 76$ $i = 19$.